What is the derivative of #f(t) = (t^2-lnt, t^2-sint ) #?

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Answer 1 · 2016-02-10T13:54:14

#f'(t)=(2t^2-tcost)/(2t^2-1)#

We know that

#x(t)=t^2-lnt#

#y(t)=t^2-sint#

Differentiate each of these with respect to #t#:

#x'(t)=2t-1/t#

#y'(t)=2t-cost#

The derivative of the parametric function is equal to

#f'(t)=dy/dx=(y'(t))/(x'(t))=(2t-cost)/(2t-1/t)#

Multiply the function by #t/t# for a simplification of:

#f'(t)=(2t^2-tcost)/(2t^2-1)#